Rigidity of representations in SO(4,1) for Dehn fillings on 2-bridge knots

Stefano Francaviglia and Joan Porti

Vol. 238 (2008), No. 2, 249–274

DOI: 10.2140/pjm.2008.238.249

Abstract

We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO₀(4,1). Here rigidity means that any discrete and faithful representation in SO₀(4,1) is conjugate to the holonomy representation in SO₀(3,1). We also show local rigidity for almost all Dehn fillings.

Keywords

fuchsian representations, global rigidity, two-bridge knot, cuspidal cohomology, Dehn filling

Mathematical Subject Classification 2000

Primary: 57M50

Milestones

Received: 1 August 2008

Accepted: 18 August 2008

Published: 1 December 2008